Question

The area between the curves $y=\tan x$,$y=\cot x$ and $x$-axis $(0\le x\le \frac{\pi }{2})$ is

• A. $\log 2$
• B. $2\log 2$
• C. $\frac{1}{2}$ $\log 2$
• D. $1$

Answer 1

Answer: (A)

$\log 2$

$y=\tan x$,$y=\cot x$ and $x$-axis $(0\le x\le \frac{\pi }{2})$
$\stackrel{\pi /4}{\underset{0}{\int }}\tan xdx+\stackrel{\pi /2}{\underset{\pi /4}{\int }}\left(\cot x\right)dx$
$-\log |\cos x|{|}_0^{\pi /4}+\log |\sin x|{|}_{\pi /4}^{\pi /2}$
$-\log \left(1/\sqrt{2}\right)+\log \left(1\right)-\log \left(1/\sqrt{2}\right)$
$\log 2$